# Prime factorization of $4700$

The calculator will find the prime factorization of $4700$, with steps shown.

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Find the prime factorization of $4700$.

### Solution

Start with the number $2$.

Determine whether $4700$ is divisible by $2$.

It is divisible, thus, divide $4700$ by ${\color{green}2}$: $\frac{4700}{2} = {\color{red}2350}$.

Determine whether $2350$ is divisible by $2$.

It is divisible, thus, divide $2350$ by ${\color{green}2}$: $\frac{2350}{2} = {\color{red}1175}$.

Determine whether $1175$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $1175$ is divisible by $3$.

Since it is not divisible, move to the next prime number.

The next prime number is $5$.

Determine whether $1175$ is divisible by $5$.

It is divisible, thus, divide $1175$ by ${\color{green}5}$: $\frac{1175}{5} = {\color{red}235}$.

Determine whether $235$ is divisible by $5$.

It is divisible, thus, divide $235$ by ${\color{green}5}$: $\frac{235}{5} = {\color{red}47}$.

The prime number ${\color{green}47}$ has no other factors then $1$ and ${\color{green}47}$: $\frac{47}{47} = {\color{red}1}$.

Since we have obtained $1$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $4700 = 2^{2} \cdot 5^{2} \cdot 47$.

The prime factorization is $4700 = 2^{2} \cdot 5^{2} \cdot 47$A.